Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x+6y &= 5 \\ 7x-4y &= -6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-4y = -7x-6$ Divide both sides by $-4$ to isolate $y$ $y = {\dfrac{7}{4}x + \dfrac{3}{2}}$ Substitute this expression for $y$ in the first equation. $-8x+6({\dfrac{7}{4}x + \dfrac{3}{2}}) = 5$ $-8x + \dfrac{21}{2}x + 9 = 5$ Simplify by combining terms, then solve for $x$ $\dfrac{5}{2}x + 9 = 5$ $\dfrac{5}{2}x = -4$ $x = -\dfrac{8}{5}$ Substitute $-\dfrac{8}{5}$ for $x$ back into the top equation. $-8( -\dfrac{8}{5})+6y = 5$ $\dfrac{64}{5}+6y = 5$ $6y = -\dfrac{39}{5}$ $y = -\dfrac{13}{10}$ The solution is $\enspace x = -\dfrac{8}{5}, \enspace y = -\dfrac{13}{10}$.